please show work Question 8 200000 points Save Answer A comp

please show work

Question 8 2.00000 points Save Answer A company owns a milling machine that it is considering replacing. Its current market value is $25,000, but it can be productively used for four more years at which time its market value will be zero. Operating and maintenance expenses are $50,000 per year. The company can purchase a new milling machine, with the same functionality as the current machine, for $90,000. In four years the market value of the new machine is estimated to be $45,000. Annual operating and maintenance costs will be $35,000 per year. Should the old milling machine be replaced using a before-tax MARR of 10% and a study period of four years? Attach File Browse My Computer Browse Content Collection

Solution

Ans:

NPV of old machine = PV of annuity of $50000 for 4 years at 10% MARR

= 50000[ (1/.1) - (1/(.1)(1+.1)^4) ] = 50000 [ 10 - 6.8301345537 ] = 158,493.272315

NPV of new machine = 90000 + P.V of annuity of 35000 for 4 years at 10% MARR - 45,000

= 90000 + 35000 [ (1/.1) - (1/(.1)(1+.1)^4) ] -45000

= 155,945.2906205

let us now calculate equivalent annual cost (EAC) of each machine = NPV/ A(t,r)

where A(t,r) = P.V annuity factor for 4 years at 10% = 3.1698654463493

EAC of old machine = 158,493.272315 / 3.1698654463493 = 50,000

EAC of new machine = 155,945.2906205  / 3.1698654463493 = 49,196.186166995

since, the EAC of new machine is less than the old one , hence, the old machine should be replaced with new one.